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Register a new userGalaxy Rotation Curves via Conformal Factors
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Added by
Adrian Ciprian Sporea
Publication date
2017
fields
Physics
and research's language is
English
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We propose a new formula to explain circular velocity profiles of spiral galaxies obtained from the Starobinsky model in Palatini formalism. It is based on the assumption that the gravity can be described by two conformally related metrics: one of them is responsible for the measurement of distances, while the other so-called dark metric, is responsible for a geodesic equation and therefore can be used for the description of the velocity profile. The formula is tested against a subset of galaxies taken from the HI Nearby Galaxy Survey (THINGS).
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A new simple expression for the circular velocity of spiral galaxies is proposed and tested against HI Nearby Galaxy Survey (THINGS) data set. Its accuracy is compared with the one coming from MOND.
We discuss the effect of a conformally coupled Higgs field on conformal gravity (CG) predictions for the rotation curves of galaxies. The Mannheim-Kazanas (MK) metric is a valid vacuum solution of CGs 4-th order Poisson equation only if the Higgs field has a particular radial profile, S(r)=S_0 a/(r+a), decreasing from S_0 at r=0 with radial scale length a. Since particle rest masses scale with S(r)/S_0, their world lines do not follow time-like geodesics of the MK metric g_ab, as previously assumed, but rather those of the Higgs-frame MK metric Omega^2 g_ab, with the conformal factor Omega(r)=S(r)/S_0. We show that the required stretching of the MK metric exactly cancels the linear potential that has been invoked to fit galaxy rotation curves without dark matter. We also formulate, for spherical structures with a Higgs halo S(r), the CG equations that must be solved for viable astrophysical tests of CG using galaxy and cluster dynamics and lensing.
The cold dark matter paradigm has been posited as the standard explanation for the non-Keplerian behavior of galaxy rotation curves, where for galaxies satisfying the Tully-Fisher relation, the mass of the dark matter halo from a large class of universal dark matter profiles ought to roughly increase linearly with radial distance at large distances, $m(r) sim r/nG$ ($G$ is the gravitational constant and $n$ is a dimensionless parameter which depends on the amount of baryonic matter $M$ within the galaxy). Despite numerous advances in modeling galaxy formation and evolution, a scientific consensus on the origin of the observed dependence of the dimensionless parameter $n = (GMa_{0})^{-1/2}$ on the mass of baryonic matter $M$ within the galaxy (the Tully-Fisher relation), and the connection of the cosmological constant $Lambda$ to the parameter $a_{0} sim (Lambda/3)^{1/2}$ remains elusive. Here, we show that Einstein Field Equations can be remolded into $ abla_{ u}mathcal{K}^{ u}_{,,mu} = 8pi GMPsi^{*}mathcal{D}_{mu}Psi$, where $mathcal{K}_{mu u}$ is a complex Hermitian tensor, $mathcal{D}_{mu}$ is a covariant derivative and $Psi$ is a complex-valued function. This avails a novel constraint, $ abla_{mu} abla_{ u}mathcal{K}^{mu u} = 0$ not necessarily available in Einsteins General Relativity. In the weak-field regime, we can readily reproduce the Tully-Fisher relation using the usual charge-less pressure-less fluid. Moreover, our approach is equivalent to a Ginzburg-Landau theory of $n$ bosons, where the order parameter is normalized as $int_{0}^{1/a_{0}} dr,4pi r^2Psi^*Psi = n$ and $1/a_{0} sim (Lambda/3)^{-1/2}$ is the cut-off length scale comparable to the size of the de Sitter universe. Our investigations provide a framework that reproduces the mass-asymptotic speed relation in galaxies within the cold dark matter paradigm.
We investigate the braneworld model with induced gravity to clarify the role of the cross-over length scale ell in the possible explanation of the dark-matter phenomenon in astrophysics and in cosmology. Observations of the 21 cm line from neutral hydrogen clouds in spiral galaxies reveal that the rotational velocities remain nearly constant at a value v_c ~ 10^{-3}--10^{-4} in the units of the speed of light in the region of the galactic halo. Using the smallness of v_c, we develop a perturbative scheme for reconstructing the metric in a galactic halo. In the leading order of expansion in v_c, at the distances r gtrsim v_c ell, our result reproduces that obtained in the Randall-Sundrum braneworld model. This inequality is satisfied in a real spiral galaxy such as our Milky Way for distances r ~ 3 kpc, at which the rotational velocity curve becomes flat, v_c ~ 7 times 10^{-4}, if ell lesssim 2 Mpc. The gravitational situation in this case can be approximately described by the Einstein equations with the so-called Weyl fluid playing the role of dark matter. In the region near the gravitating body, we derive a closed system of equations for static spherically symmetric situation under the approximation of zero anisotropic stress of the Weyl fluid. We find the Schwarzschild metric to be an approximate vacuum solution of these equations at distances r lesssim (r_g ell^2)^{1/3}. The value ell lesssim 2 Mpc complies well with the solar-system tests. At the same time, in cosmology, a low-density braneworld with ell of this order of magnitude can mimic the expansion properties of the high-density LCDM (lambda + cold dark matter) universe at late times. Combined observations of galactic rotation curves and gravitational lensing can possibly discriminate between the higher-dimensional effects and dark matter.
In this work we derive a generalized Newtonian gravitational force and show that it can account for the anomalous galactic rotation curves. We derive the entropy-area relationship applying the Feynman-Hibbs procedure to the supersymmetric Wheeler-DeWitt equation of the Schwarzschild black hole. We obtain the modifications to the Newtonian gravitational force from the entropic formulation of gravity.
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